Magnetic excitations of intermediate coupling antiferromagnets

Intermediate coupling systems exhibit fascinating phenomena emerging from the interplay of charge, spin, and orbital degrees of freedom. Among these, 4d and 5d electron systems, such as strontium iridates and their thin films, serve as model platforms for studying these interactions. The continuous development of high-resolution spectroscopic techniques, such as inelastic neutron scattering and resonant inelastic X-ray scattering (RIXS), necessitates advanced theoretical frameworks. While semiclassical approaches, like Landau-Lifshitz dynamics, provide crucial insights into spin models, the weak Mott insulating behavior in the intermediate coupling regime demands novel methodologies to incorporate charge fluctuations. To address these challenges, we developed a semiclassical methodology capable of large-scale simulations (over 10⁴ sites) of dynamical properties at finite temperatures across a broad range of U/t values in the Fermi-Hubbard model. Applying this numerical approach and the theoretical analysis based on the random phase approximation to the bilayer Hubbard model with spin-orbit coupling, we examined magnetic excitations in Sr₃Ir₂O₇, an intermediately correlated antiferromagnet. On-site electron repulsion induces preformed excitons in a paramagnetic band insulator, culminating in triplet exciton condensation and antiferromagnetic order. The RIXS spectrum reveals a distinctive longitudinal mode associated with this condensation. Additionally, we extended the low-energy theory of magnetic Raman scattering to the intermediate coupling regime, providing a theoretical explanation for experimental results. Raman scattering captures a longitudinal mode below the two-magnon excitation threshold and tracks its softening under pressure, signaling a quantum phase transition. Our numerical approach, applicable to complex geometries, also uncovers noncoplanar magnetic orders induced by exciton condensation in bilayer triangular lattices. This work advances understanding of correlated systems and their rich dynamical properties in the intermediate coupling regime.